where \(d_W(\mu _n,\mu )\)  denotes the Wasserstein distance of the measure \(\mu _n\)  and \(\mu \)  (see [1]}). Since \(d_W(\mu _n,\mu )\rightarrow 0\)  (e.g., [2]}), there is \(n_2\in \mathbb {N}\)  satisfying
\(d_W(\mu _n,\mu ) < \tfrac{{\varepsilon }}{2L}\quad \text{for all }n>N_2.\) 
